Mirror Modifier Weights Not Working
After a bit of digging when I ran into this issue again, I found out that for whatever reason, the vertex group for that particular bone didn't transfer to the mirrored mesh. As a result, the weights for the mirrored object were there, but the wrong bone was controlling it. In my case, I mirrored to the right side, and that part of the mesh was being controlled by the left side. Here's the solution I found:


Figure out what the missing vertex group(s) are in the vertex group panel. Watch for the one(s) that doesn't have a counterpart for the other side (For example: if there's a hair1.L and no hair.R, you've found one). Select the one for the side that you do have.
Use the grey arrow below the plus and minus buttons to copy the vertex group within the object and lock the original version.
Rename the copy to the bone you want to control it with (For example: hair.L_copy would be renamed to hair.R).
While the bones have control over their intended weights, they will still control the wrong side. Go ahead and fix this in weight paint mode by subtracting from anything that they don't need. Don't forget to unlock any vertex groups that you locked before.